Conventionally, an apparatus for controlling the idle speed of an internal combustion engine has been proposed in which an auxiliary air control valve is provided in an auxiliary air path bypassing a throttle valve and the opening degree of said auxiliary air control valve during idle operations is controlled, thereby, the idle speed is controlled by controlling the amount of auxiliary air supplied to the engine via said auxiliary air path (Japanese Unexamined Utility Model Publication No. 1-179148).
Said auxiliary air control valve is of the solenoid type and the valve opening degree thereof is controlled according to the duty ratio (the time ratio expressed as a percentage, of the pulse width to the period, when the opening degree is controlled by controlling the pulse width of the drive pulse signal for valve opening fed at a constant period of time).
Further, the duty ratio ISC.sub.ON (%) fed to said auxiliary air control valve is calculated for example according to the following equation: EQU ISC.sub.ON =ISC.sub.TW +ISC.sub.CL
Here, ISC.sub.TW is the basic control value which is set referring to a map in the ROM based on the engine cooling water temperature Tw. ISC.sub.CL is the feedback correction value which is set, based on the result of comparison of the engine rotational speed with the target idle speed under the idle speed feedback control conditions so that the actual engine rotational speed approaches the target idle speed, for example, with the proportional integral control.
Specifically, the target idle speed N.sub.SET is compared with the actual engine rotational speed Ne, and, if for example the engine rotational speed is lower than the target idle speed, said duty ratio ISC.sub.CL is gradually increased by the integration operation amount, and also, said duty ratio ISC.sub.CL is corrected to be increased according to the proportional operation amount depending on the deviation of the actual engine rotational speed from the target idle value.
Thus, in the conventional idle speed control, the response characteristic of control and the suppression of overshoot generation were balanced by gradually varying the auxiliary air flow rate over a long time duration with the proportional and integral control while monitoring the change in the engine rotational speed. This is because, when the engine rotational speed was decreased, for example, due to the application of load, the amount of increase of the auxiliary air flow rate finally required was not known at the time of increasing the auxiliary air flow rate matching with the applied load.
That is, during the period between the application of the control signal to the auxiliary air control valve and the result of actual control affecting the engine rotational speed, there are the processes of the auxiliary air being sucked into the cylinder via the manifold, the air-fuel mixture sucked into the cylinder undergoing explosion, the angular velocity changing due to the pressure of this explosion, the period of rotation signal generation changing thereby, and this change being detected as a change in the rotational speed. Therefore, even when the auxiliary air control valve is controlled, there is a response delay time until such a control is detected as an actual change in the engine rotational speed.
As a result, in the condition that the finally required auxiliary air flow rate is not known since it is necessary to repeat the steps of gradually varying the auxiliary air flow rate over a considerably long time duration with the proportional and integral control, confirming a result of this control as the change in the actual rotational speed, and then adjusting the auxiliary air flow rate after determining the next control direction, it is not possible to set the feedback response time faster than said response delay time and also the overshoot will become large if the rate of change of the auxiliary air flow rate is made large.
Thus, according to the conventional idle speed control, it was difficult to improve the response characteristic of the control and to sufficiently suppress the generation of undershoot, for example, at the time a load is applied, it was necessary to set a relatively high target idle speed so that the target idle speed did not become lower than the rotational speed at the engine stalling limit even when said undershoot occurred, and it was difficult to realize the reduction of target idle speed for improving the fuel consumption because such reduction was restricted by the magnitude of said undershoot.
Japanese Unexamined Patent Publication No. 63-75334, etc. propose technology to carry out the control of engine rotational speed by the linear modeling of the dynamic behavior of an internal combustion engine as technique for improving the response characteristic of the feedback control.
Specifically, the feedback control amount is determined based on the numeric model obtained by digitizing, by sampling at each constant crank angle the dynamic physical model of the engine made by using the intake pressure and the rotational speed.
However, since the model obtained by digitizing by sampling at each constant crank angle was used in said technique, there was the problem that a processor capable of high speed computations for carrying out complex calculations is required in an actual control.
In view of the above, the inventors have previously proposed an apparatus where the response characteristic can be improved without complex calculations by setting the output torque required from the engine so as to obtain the target idle speed and controlling the opening degree of the auxiliary air control valve so as to obtain the required auxiliary air flow rate corresponding to the required output torque (Japanese Unexamined Patent Publication No. 5-240090).
However, there are limitations to obtain a higher response characteristic of idle speed control by only improving the response characteristic of the auxiliary air control valve, therefore a further improvement is needed.
That is, there are the problems that even if the auxiliary air control valve is controlled with a fast response speed so that the required auxiliary air flow rate corresponding to the required output torque is achieved, there is a response delay from the time when the auxiliary air control valve is controlled until the required auxiliary air flow rate is obtained, and response speed is particularly slow in the case of stepping motors generally used for driving an auxiliary air control valve (the time delay from the application of the drive signal until the auxiliary air control valve is set to the desired opening degree is too large). In addition, in the case of an electronically controlled fuel injection type internal combustion engine, even if the auxiliary air control valve is controlled so that the required auxiliary air flow rate is achieved, there is a response delay from the detection of said required auxiliary air flow rate until the correction control of the fuel injection amount is carried out. Therefore, the initial engine rotational speed variations at the time of Icad change caused by said response delay can not be avoided by merely improving the response characteristic of the auxiliary air control valve.